A Collocation Method for the Solution of Volterra Integro-differential Equations Based on Orthogonal Polynomials

Abstract

In this research, we constructed collocation methods for approximating the solutions of Volterra integro-differential equations using Legendre polynomials, Chebyshev polynomials, and Laguerre polynomials as basis functions. The Standard Collocation Method (SCM) is used to determine the desired collocation points within an interval say, to solve sample problems ranging from linear first to second-order Volterra integro-differential (VIDEs) equations using the methods. developed The method was implemented using MAPLE 17 computer software and the obtained results are compared with the exact solution for the orthogonal polynomials. Results revealed that Laguerre Polynomials has the best accuracy for the first-order VIDE while Legendre polynomial has the best approximation for the second-order VIDE. However, both polynomials offer good approximations.